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NEW YORK — The Celtics have a chance to close out their first-round series in a hurry, up three games to none over the Knicks after last night’s 113-96 win.

The Celtics are 8-11 in closeout games going back to the 2008 playoffs. They’ve never swept a team in the new Big Three era.

Their two chances came during last season’s playoffs when they went up three games on the Heat in the first round (dropping Game 4 on the road) and the Magic in the conference finals (losing Game 4 at home and Game 5 in Orlando).

“We still have to play the games,’’ Kevin Garnett said. “This is a team that can put up a lot of points and they’re playing at home. So we’ll focus on [Game 3], enjoy tonight, then get ready for Game 4.’’

Miami is also up, 3-0, in its series with Game 4 tomorrow in Philadelphia. If both the Celtics and Heat sweep, the earliest their second-round meeting could start would be next Sunday, giving both teams six days to rest.

“It’s very important,’’ Paul Pierce said. “For one, if we get the job done, it gives an old veteran team a chance to rest going into the second round, which is always great. Hopefully, some of the nicks and knacks on some of the other guys’ bodies can heal.’’

The Knicks are playing their first playoff series in seven years, when they were swept by the Nets.

“We want to finish this,’’ Glen Davis said. “We’re going to do all we can. We know it’s not going to be easy. They’re going to come out and play. They have pride, and I know just the way they feel. They’re going to want to win a game. At least a game.’’

Healthy optimism

The Celtics aren’t ruling out Shaquille O’Neal for the rest of the postseason — or the rest of this first-round series, for that matter — but they also aren’t sure when he’ll be healthy enough to see the floor.

O’Neal, who missed all but one game the last three months of the season with an inflamed right Achilles’ tendon, traveled to New York Thursday, a sign that the team thinks he’s closer to returning.

“He’s just feeling better and he’s closer,’’ said coach Doc Rivers. “I don’t know what he has to show me. He’s not ready to play yet, but he’s closer. So the fact that he’s getting closer, you bring him on the road.’’

O’Neal, 39, played in 34 regular-season games.

“I don’t think he has an expiration date,’’ Rivers said. “Maybe he does. We all do, I guess.’’

Taking precautions

Jermaine O’Neal has started wearing a brace on his sprained right wrist during off days, a precaution after injuring it in the second quarter of Game 2.

“To make sure I didn’t open a door wrong or irritate it,’’ he said. “It was one of those situations where I took a charge and put my hand back before I fell and irritated it a little bit. But I’m fine.’’

The wrist is not a concern for him or Rivers. “Fortunately, he’s never been that great with that hand anyway,’’ Rivers said. “He can still defend and rebound and do all the other stuff, so that’s good.’’

O’Neal scored 12 points in the series opener but took just three shots in 20 minutes in Game 2. Last night, O’Neal shot 3 of 7 for 6 points, with three rebounds and five fouls in 27 minutes.

Rivers decided to sit O’Neal in the second half of Game 2, primarily so he could use Davis in a smaller rotation. O’Neal and Rivers talked after the game to make sure they were on the same page.

“I think it was a great confidence-booster for Baby, being in there late, obviously, after struggling the first game,’’ O’Neal said. “This is about a team effort, it’s not about me getting more minutes.

“You’ve got to be locked into whatever the team needs, and I’m with Doc. Doc talked to me after the game and he explained why and I was like, ‘Coach, you made the right decision.’ ’’

Billups may be done

Amar’e Stoudemire made it on the court for Game 3 last night. Chauncey Billups did not.

Billups, the Knicks point guard, missed his second straight game after straining his left knee in the final minutes of Game 1 against the Celtics, and his availability for this series continues to look doubtful.

“Just so frustrating, coming here and knowing I can’t play today,’’ Billups said. “It’s tough, man. This is the time of the season that I live for, so it’s really tough.

“I’m just continuing trying to do the best that I can do to get back on the floor. But it’s just . . . simply it’s just not ready.’’

Billups worked out yesterday morning, doing exercises in a pool, but he knew that trying to play would be futile.

“It’s tough. Walking around, I’m fine now. But as you see in this series, there’s not a lot of walking being done.’’

Being injured in the postseason isn’t new to Billups. With the Pistons, he hurt his ankle in 2003 and missed time, and he hurt his groin in 2008 and missed time. In 2008, Billups’s Pistons lost to the Celtics in the Eastern Conference finals.

“I felt like if I played in that series against them, we would have beat them,’’ Billups said. “I feel like if I play in this series, we have a chance to beat them. It’s crazy. It’s frustrating.’’

Asked if he could return in this series, Billups said, “I think it’s maybe a chance. But I don’t know that to be 100 percent sure and true. But I guess we’ll kind of go day to day, see how it goes.’’

Ab jab

Davis heard about the subtle jab Stoudemire took at his weight, but shook it off. Stoudemire told reporters that Davis’s “core is not really as tight as it should be.’’ Davis, who weighs 289 pounds, said, “I ain’t never had no abs. Why would I worry about that? I’ve never in my life had abs. Since I was a baby, never had abs. No six-pack, nothing.’’

Amalie Benjamin of the Globe staff contributed to this report. Julian Benbow can be reached at jbenbow@globe.com.